Introduction to octonion and other non-associative algebras in physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Series: | Montroll memorial lecture series in mathematical physics
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 136 S. Ill. |
| ISBN: | 0521472156 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to octonion and other non-associative algebras in physics |c Susumu Okubo |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XI, 136 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Montroll memorial lecture series in mathematical physics |v 2 | |
| 600 | 1 | 4 | |a Montroll, E. W |
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| 650 | 4 | |a Mathematische Physik | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface page xi
1 Introduction 1
2 Non associative algebras 11
2.1 Definition and examples 11
2.2 Multiplication table 13
2.3 Associator and flexible algebra 15
2.4 Power associative algebra 17
2.5 Alternative algebra 18
2.6 Algebras A± 19
3 Hurwitz theorems and octonions 21
3.1 Hurwitz algebra 21
3.2 Left and right multiplication operations 24
3.3 Dimensions of Hurwitz algebras 26
3.4 An application of octonion algebra to instanton 31
3.5 Derivation Lie algebras 38
4 Para Hurwitz and pseudo octonion algebras 40
4.1 Para Hurwitz algebras 40
4.2 Pseudo octonion algebra 41
4.3 Miscellaneous theorems on composition algebras 47
5 Real division algebras and real Clifford algebra 51
5.1 Division algebras 51
5.2 Application to real Clifford algebra 53
5.3 Dimensional regularization and non associative Dirac algebra 61
6 Clebsch Gordan algebras 64
6.1 SU(2) case 64
ix
x Contents
6.2 Homomorphism (W »¦ W2) 68
6.3 G2 and split Cay ley algebra 74
7 Algebra of physical observables 80
7.1 Jordan product 80
7.2 Heisenberg approach 82
7.3 Non linear Schrodinger equation 85
8 Triple products and ternary systems 89
8.1 Introduction 89
8.2 Alternative triple systems and Hurwitz algebras 91
8.3 Zorn s vector matrix octonion algebra and the Cayley
Dickson process 95
8.4 Octonionic triple system 100
8.5 Application to Yang Baxter equation 105
8.6 Nambu s dynamical equation and Lie triple system 110
9 Non associative gauge theory 115
9.1 Digression of Yang Mills gauge theory 115
9.2 Non associative gauge theory 118
9.3 Einstein s relativity as a non associative Chern Simon theory 122
10 Concluding remark 130
References 131
Index 135
|
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| isbn | 0521472156 |
| language | English |
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| physical | XI, 136 S. Ill. |
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| series | Montroll memorial lecture series in mathematical physics |
| series2 | Montroll memorial lecture series in mathematical physics |
| spelling | Okubo, Susumu 1930-2015 Verfasser (DE-588)119068842 aut Introduction to octonion and other non-associative algebras in physics Susumu Okubo 1. publ. Cambridge Cambridge Univ. Press 1995 XI, 136 S. Ill. txt rdacontent n rdamedia nc rdacarrier Montroll memorial lecture series in mathematical physics 2 Montroll, E. W Algèbres associatives ram Physique mathématique ram Mathematische Physik Cayley algebras Mathematical physics Nonassociative algebras Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Nichtassoziative Algebra (DE-588)4297760-5 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s Nichtassoziative Algebra (DE-588)4297760-5 s DE-604 Montroll memorial lecture series in mathematical physics 2 (DE-604)BV008907205 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006971440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Okubo, Susumu 1930-2015 Introduction to octonion and other non-associative algebras in physics Montroll memorial lecture series in mathematical physics Montroll, E. W Algèbres associatives ram Physique mathématique ram Mathematische Physik Cayley algebras Mathematical physics Nonassociative algebras Mathematische Physik (DE-588)4037952-8 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4297760-5 |
| title | Introduction to octonion and other non-associative algebras in physics |
| title_auth | Introduction to octonion and other non-associative algebras in physics |
| title_exact_search | Introduction to octonion and other non-associative algebras in physics |
| title_full | Introduction to octonion and other non-associative algebras in physics Susumu Okubo |
| title_fullStr | Introduction to octonion and other non-associative algebras in physics Susumu Okubo |
| title_full_unstemmed | Introduction to octonion and other non-associative algebras in physics Susumu Okubo |
| title_short | Introduction to octonion and other non-associative algebras in physics |
| title_sort | introduction to octonion and other non associative algebras in physics |
| topic | Montroll, E. W Algèbres associatives ram Physique mathématique ram Mathematische Physik Cayley algebras Mathematical physics Nonassociative algebras Mathematische Physik (DE-588)4037952-8 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| topic_facet | Montroll, E. W Algèbres associatives Physique mathématique Mathematische Physik Cayley algebras Mathematical physics Nonassociative algebras Nichtassoziative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006971440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT okubosusumu introductiontooctonionandothernonassociativealgebrasinphysics |